This is the same program that has sharpening that goes up to 500%
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MikeWMay 3 '11 at 3:55

1

I believe the jokes are actually the right answer. I remember that in an older version of Photoshop (3, maybe — not CS3, but Photoshop 3), 11 was the top value. And remember, although it's a gigantic corporately-produced product now, the program was originally the handiwork of a couple of genius programmers, a class of people notably fond of such humor. And then 12 was added later, just like the XKCD comic.
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mattdmMay 3 '11 at 11:57

3 Answers
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First off, realize that those numbers are 100% arbitrary... a 6 out of 12 on one application may or may not match a 50/100 on another application, even though they are mathematically the same. So don't try to compare those values across applications.

With that in place... what that control is adjusting are the "quantization tables" of the compression algorithm. Usually the are the Luminance and Chrominance quantization tables. These tables describe how much of each type of information is discarded by the compression engine, for different types of repeating patterns. Forexample a "fine" QT might have a very low number in all parts of the table, saying no matter how often a pattern repeats, don't discard it, where as the opposite table would have larger numbers in the areas of the table that are represent frequently occurring patterns. Basically saying "this is a common pattern, you can compress it down a lot more, it's not as important to the image."

Different things that do compression have different sets of tables stored in them. My camera for example has 2 (Fine and Coarse) per jpeg size. (at least I'm betting that Small Fine doesn't use the same tables as Large Fine... but they might!) I've seen a couple cameras that had 4 levels (Low, Normal, Fine, SuperFine). Photoshop traditionally has 13 (0-12), Lightroom claims 101 (1-101) (more on that in a moment.) and I've seen other tools with anywhere from 5 (1-5) to 256! (0-255).

So let's start with Photoshop's 13 levels. Basically they have 13 sets of QTs built into the application which make up spectrum of more and more detail. 0 is horrid, compressing things to well past anything useful. 12 is equally unusable, but for the opposite reason, it can actually result in files LARGER than what would be needed to represent the image in a loss-less compression such as PNG, or even in an uncompressed format like BMP! So why is it there? Well, the commonly accepted reasoning, and I've seen this over and over, was that the original PS team expected most people to use 0-10, and 11 and 12 were left in place for "research" or for bridging over to another application to let it do the compression. (though if you're going to do that, why even export as jpg? just export TIFF or something.)

Now, lightroom's 101 step claim got torn apart pretty well a while back by Jeffrey Friedl. There are two big findings there.

LR maps that 101 values into just 13 different QTs, each 7 or 8 points wide. 93, 95, 99, and 100 for example, all use the same values.

My experience is that 95 is different to 100 in LR, so it may have some other effect as well.
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Rowland Shaw♦May 3 '11 at 8:25

@Rowland, I just exported the same image as 95, 99, and 100. The three files are exactly the same size, down to the byte. An image level comparison in photoshop (pixel subtraction) shows exactly the same image between all three. 92 is noticeably different, ditto 80, 50 and 0. I'd be willing to bet the three files are byte for byte the same excluding the render date meta data.
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cabbeyMay 3 '11 at 20:47

I think you are not explaining quantization tables right. It has nothing to do with repeated remembered patterns: nothing in JPEG works that way. The QT has to do with rounding off the numbers after it converts to frequency domain. Higher frequencies can be rounded severely or even discarded, and you get the characteristic jpeg artifacts. Several standard tables are used so it doesn't have to include it in the file.
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JDługoszDec 3 '14 at 23:36

I don't know what PS is doing with those reportedly bloated files, but using a non-QT that doesn't intentionally munge the values (known as virtually lossless) will generally give 4:1 compression on detailed scenes like landscapes. True lossless compression via any of several means will do about 2:1.
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JDługoszDec 3 '14 at 23:41

I can't provide an answer for why there is the option to go to 12 - but I can provide an example of the different qualities.

I have taken these directly from one of my lecturer's slideshows, it's not my own work.
The images were used to illustrate that there is no difference between JPEG quality 12 and 11 other than file size (at least not one that is visible to the human eye). Therefore 11 is the better option because of the smaller file size.

I know it's not the answer to your question, but thought it might be a little bit of help.

Hmm, actually just looking at it again it is quite clear that the colours are a little bit depper in the 12 than the 11. So I guess that negates my whole argument... University is for chumps!
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ChardMay 3 '11 at 10:07

2

Could be the imgur compression algorithm in action.
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AndresMay 3 '11 at 14:22

Jeffrey Friedl has a great analysis of the JPG quality settings and output from Lightroom, and in his results the output when compared between Lightroom and Photoshop varies... even Lightroom's 0-100 scale does not correspond to the 0-100 scale in Photoshop's "Save for Web" dialog.